"We have to run and fight. It's not enough to just pass. Champions League is another situation - different from the championship," Mancini said after Wednesday's fortuitous 1-1 home draw against German champions Borussia Dortmund.
"It's not enough to just have quality," the Italian added after the draw followed a 3-2 defeat to Real Madrid in their Champions League opener.
City have splashed out over €440 million in the past four seasons, the most of any European club, but success on the continent is so far proving elusive.
City's Abu Dhabi owners and their heavy investments were initially rewarded with the FA Cup in 2011, their first piece of silverware in 35 years, and then in May when they clinched their first top flight league title since 1968.
However, Mancini's men have started the new season slowly and trail league leaders Chelsea by four points, while in the Champions League, their chances of a first knockout stage appearance hang in the balance.
"I know the problem and I will resolve it very quickly," Mancini said.
His side will quickly need to regain their form in the elite European competition, where they lie third in Group D and next play back-to-back matches against bottom club Ajax Amsterdam and will likely require to win both matches to stay in the hunt.
"If we want to play in the Champions League, we have to play better," Mancini added.
Last season, City failed to reach the knockout stage despite notching up 10 points from their six group games.
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